Full Idea
Kripke showed that the Barcan formula ∀x□A⊃□∀xA and its converse fail in models which require varying domains.
Gist of Idea
The Barcan formulas fail in models with varying domains
Source
report of Saul A. Kripke (A Completeness Theorem in Modal Logic [1959]) by Timothy Williamson - Truthmakers and Converse Barcan Formula §1
Book Reference
-: 'Dialectica' [-], p.256
A Reaction
I think this is why I reject the Barcan formulas for metaphysics - because the domain of metaphysics should be seen as varying, since some objects are possible in some contexts and not in others. Hmm…
Related Ideas
Idea 15135 If the domain of propositional quantification is constant, the Barcan formulas hold [Williamson]
Idea 9449 The plausible Barcan formula implies modality in the actual world [Bird]